Abstract: Graph decompositions are vital in the study of
combinatorial design theory. A decomposition of a graph G is a
partition of its edge set. An n-sun graph is a cycle Cn with an edge
terminating in a vertex of degree one attached to each vertex. In this
paper, we define n-sun decomposition of some even order graphs
with a perfect matching. We have proved that the complete graph
K2n, complete bipartite graph K2n, 2n and the Harary graph H4, 2n have
n-sun decompositions. A labeling scheme is used to construct the n-suns.
Abstract: Graph decompositions are vital in the study of combinatorial design theory. Given two graphs G and H, an H-decomposition of G is a partition of the edge set of G into disjoint isomorphic copies of H. An n-sun is a cycle Cn with an edge terminating in a vertex of degree one attached to each vertex. In this paper we have proved that the complete graph of order 2n, K2n can be decomposed into n-2 n-suns, a Hamilton cycle and a perfect matching, when n is even and for odd case, the decomposition is n-1 n-suns and a perfect matching. For an odd order complete graph K2n+1, delete the star subgraph K1, 2n and the resultant graph K2n is decomposed as in the case of even order. The method of building n-suns uses Walecki's construction for the Hamilton decomposition of complete graphs. A spanning tree decomposition of even order complete graphs is also discussed using the labeling scheme of n-sun decomposition. A complete bipartite graph Kn, n can be decomposed into n/2 n-suns when n/2 is even. When n/2 is odd, Kn, n can be decomposed into (n-2)/2 n-suns and a Hamilton cycle.